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Some Exponential Inequalities for Negatively Orthant Dependent Random Variables

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Abstract

In the paper, we establish some exponential inequalities for non-identically distributed negatively orthant dependent (NOD, for short) random variables. In addition, we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random variables. As an application, the Kolmogorov strong law of large numbers for identically distributed NOD random variables is obtained. Our results partially generalize or improve some known results.

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Acknowledgments

The authors are most grateful to the Editor and anonymous referee for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Xue-jun Wang & Shu-he Hu

Authors
  1. Xue-jun Wang
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  2. Shu-he Hu
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Corresponding author

Correspondence to Xue-jun Wang.

Additional information

This paper is supported by the National Natural Science Foundation of China (Nos. 11671012, 11871072, 11701004, 11701005), the Natural Science Foundation of Anhui Province (Nos. 1808085QA03, 1908085QA01, 1908085QA07), and the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0001, KJ2019A0003).

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Wang, Xj., Hu, Sh. Some Exponential Inequalities for Negatively Orthant Dependent Random Variables. Acta Math. Appl. Sin. Engl. Ser. 36, 847–856 (2020). https://doi.org/10.1007/s10255-020-0985-5

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  • DOI: https://doi.org/10.1007/s10255-020-0985-5

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